Results 1 to 3 of 3

Math Help - Accumulation points and finding them

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    30

    Accumulation points and finding them

    This is the definition of accumulation point that my book gives:

    A is an accumulation point of S \subset \mathbb{R}, \forall \epsilon > 0, S \bigcap B(A;\epsilon) is infinite.

    The book I have gives horrible examples on what accumulation points actually are (contradicting itself two out of the three times), but never actually gives instructions on how to find the points.

    This is the question I have to solve:

    Find the accumulation points of S = \left\{\frac{2}{n} + (1 - \frac{1}{n})cos(\frac {n\pi}{2}) : n \in\mathbb{N}\right\}

    Can anyone help to actually explain to me, in english, what an accumulation point is? I tried Wikipedia but it's more of this meaningless jargon.

    Hopefully, understanding what it is I'm looking for will show me how to answer this question. If not, I could use help there too.
    Last edited by HeirToPendragon; February 15th 2009 at 06:32 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Dec 2008
    Posts
    30
    This is what I've come to thus far on a different forum:

    It looks like it will just go back to looking like a typical cosine graph (which I guess is to be expected since 2/n and 1/n go to 0)

    So if we set n_{k} = 2k \Rightarrow\left\{\frac{1}{k} + (1 - \frac{1}{2k})cos(k\pi) \right\} \rightarrow (-1,1)

    and n_{k+1} = 2k+1 \Rightarrow\left\{\frac{2}{2k+1} + (1 - \frac{1}{2k+1})cos(\frac{\pi(2k+1)}{2}) \right\} \rightarrow {0}

    Ok I think I broke my brain. Did any of that make sense? If it does, are the accumulation points for the set -1,0,1?

    If it didn't make any sense (because I'm supposing it doesn't at this point, I've had a bit of a head cold all weekend), where should I actually be heading?
    Last edited by HeirToPendragon; February 15th 2009 at 09:20 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    30
    *delete*
    Last edited by HeirToPendragon; February 15th 2009 at 09:20 PM. Reason: double post... don't know how to delete
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. accumulation points or limits points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 27th 2010, 03:20 AM
  2. [SOLVED] No set (0,1) as accumulation points
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: October 8th 2010, 03:57 AM
  3. accumulation points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 19th 2009, 02:56 PM
  4. Accumulation Points
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 26th 2009, 02:19 PM
  5. Replies: 3
    Last Post: January 11th 2009, 12:49 PM

Search Tags


/mathhelpforum @mathhelpforum